Two of the activists, who were both shot, died at a district hospital in Natore, said Mohammad Faridul Islam Khan, the officer in charge of a nearby police station. He said that the police were still investigating the deaths.

Dozens of activists from the rival political parties were facing off in Natore when the police arrived, throwing pieces of broken bricks at one another. The police charged at the protesters with batons to break up the violence, Mr. Khan said.

Another opposition supporter died in Rajshani in clashes with the police when members of the Bangladesh Nationalist Party tried to disrupt a rally by the governing party, a police official in the area said. And in the nearby district of Chapai Nawabganj, the police said, opposition supporters and members of Jamaat-e-Islami, the largest Islamic party in the country, violated a ban on protests and attacked the police and security officers, who fired back. One protester was killed.

The clashes occurred after several days of tension between the Nationalist Party, which boycotted last year’s elections in protest of the Awami League’s decision against a caretaker government to oversee the voting, as had been the case since 1996. Pro-government candidates ran unopposed in more than half of the parliamentary districts.

On Sunday, the police announced a ban on rallies in the capital, Dhaka. On Monday, Begum Khaleda Zia, the leader of the Bangladesh Nationalist Party, called for a countrywide blockade of roads, railways and waterways.

Mrs. Zia, a former prime minister of Bangladesh, has been in her party’s office in Dhaka since Saturday with about 100 police officers outside. Sheikh Hasina, the current prime minister, denied that Mrs. Zia was being held there, adding that she was free to go, according to the state-run news agency Bangladesh Sangbad Sangstha.

But Mrs. Zia took issue with Ms. Hasina’s contention when she spoke to members of the news media on Monday afternoon.

“If I’m not confined, then why did they block the entrance of my office?” she said in televised comments. “It’s not only me. The whole country is in confinement.”